Use the theoretical method to determine the probability of the following outcome and event. State any assumptions made. Tossing two coins and getting either one head or two heads A. Assuming that each coin is fair and is equally likely to land Assuming that each coin is fair and is equally likely to land heads or tails, the probability is \( \frac{1}{2} \). Assuming that each coin is fair and is equally likely to land C. heads or tails, the probability is \( \frac{3}{4} \). Assuming that each coin is fair and is equally likely to land D. heads or tails, the probability is \( \frac{4}{3} \)

To determine the probability of getting either one head or two heads when tossing two fair coins, we can use the theoretical method. ### Step 1: Identify the Sample Space When tossing two coins, the possible outcomes are: 1. HH (two heads) 2. HT (one head, one tail) 3. TH (one head, one tail) 4. TT (two tails) Thus, the sample space \( S \) is: \[ S = \{ HH, HT, TH, TT \} \] ### Step 2: Count the Favorable Outcomes We are interested in the outcomes where we get either one head or two heads. The favorable outcomes are: 1. HH (two heads) 2. HT (one head, one tail) 3. TH (one head, one tail) So, the favorable outcomes are: \[ \{ HH, HT, TH \} \] ### Step 3: Calculate the Probability The total number of outcomes in the sample space is 4 (as listed above). The number of favorable outcomes is 3 (HH, HT, TH). The probability \( P \) of getting either one head or two heads is given by the formula: \[ P(\text{one head or two heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{4} \] ### Conclusion Thus, the probability of getting either one head or two heads when tossing two fair coins is \( \frac{3}{4} \). ### Assumptions Made 1. Each coin is fair, meaning the probability of landing heads (H) or tails (T) is equal (i.e., \( P(H) = P(T) = \frac{1}{2} \)). 2. The tosses of the coins are independent events, meaning the outcome of one coin does not affect the outcome of the other coin. ### Answer C. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is \( \frac{3}{4} \).